Let a compnay developed a new product. A buyer buys x units of this product and y units of another good. The consumer utility is given by u = x^(1/2)y^(1/2)
But, with probability 1/2, the new product has some problem and delivers only 1/4 of the claimed flow of services which the utility is u = [(1/4)x]^(1/2)y^(1/2)
Both goods cost 1 per unit and the consumer's income is 32.
Q1) What's the cosumer's expected flow of services when getting x units of the new product?
Q2) Hypothetically the new product delivers its expected flow of services with certainty. What are the optimal consumption choices?